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An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder.
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Models can be constructed using long-range interactions for a many-body localized phase with zero particle number and energy conductivities, but with infinite saturation entanglement; an example pointed out to the authors by V. Oganesyan and D. Huse is the evolution of an initial σ x \sigma^{x} product state in a longitudinal-field Ising Hamiltonian with exponentially decaying effective interaction
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